This paper introduces a novel type system that can infer an object's composition of traits (mixin-style classes) according to its usage in a program. Such "trait inference" is achieved with two new ideas. First, through a polyvariant treatment of assignments (a := b) and implied field sub-assignments, assignment can usefully encode trait extensions, method calls, overriding, and so on. Second, rather than unify term types or solve inequality constraints via intersection, we instead propagate trait requirements "backward" to assignees, ensuring that trait requirements are compatible only for terms used in the program. We show how this system is feasible without type annotations while supporting mutability, sub-typing, and parametricity.